What I do not understand is that there is no voltage anymore*** at point 2 (and at point 1, let's say if a seq runs, I have logically a fluctuating voltage). I do not understand how CV is possible if, at the input of the opAmp, no voltage is present.
And when I measure current at 2, it is not even changing.
This is why I was wondering what kind of signal is then outputed by the res, and what kind of signal is then measurable at 2.

***Rectification:
I did new measurement to try to understand and with my DMM I get some mV at 2, so the voltage is not inexisting (very confusing if this was at zero !). I thought the voltage would then be re-amplified via opAmp, but it looks like the opAmp just works fine with voltages in mV scale.
I am going to re-read with more concentration the opAmp wiki pages.

It is also obvious that I do not know how to measure current (I measured it like I did with voltages but not in series: really stupid !). The only thing I did right was to connect the DMM cables from volt/ohm to ampere connection !). It is the kind of detail which is very important !
I found now pages on the web explaining how to measure current, so I will do new measurements.

"Reading current is one of the trickiest and most insightful readings in our world of embedded electronics. It’s tricky because you have to measure current in series. Where voltage is measure by poking at VCC and GND (in parallel), to measure current you have to physically interrupt the flow of current and put the meter in line".

Wanting to add CV to anything and not knowing these basics makes people loose their time with my doubts, issues and so on. I apologize !
On the other hand I do learn very much here.
I hope though it will help other beginners.
My advice: first start with the basics !

The fuse was dead for current measurement on my DMM.
Now I can measure current too.

"Remember: When you’re done using the meter, always return the meter to read voltage (return the probes to the voltage port, set the meter to read the DC voltage range if necessary). It’s common to grab a meter and begin to quickly measure the voltage between two pins. If you have left your meter in ‘current’ mode, you won’t see the voltage on the display. Instead you’ll see ‘0.000’ indicating that there is no current between VCC and GND. Within that split second you will have connected VCC to GND through your meter and the 200mA fuse will blow = not good. So before you put the meter down for the night, remember to leave your meter in a friendly state.

Measuring current can be tricky the first couple of times. Don’t worry if you blow the fuse - we’ve done it dozens of times! "

I checked the opAmp at wiki but I will need to read again (and again), plus I found quite similar circuits than the one I found in a book on the web as there are quite basics.
My goal being to understand what exactly happens and what current does / what voltage does in the circuit.

It's not easy to learn, the "pros" spend years in school to learn this stuff, and it does take a lot of re-reading. Starting with basics definitely helps, you might want to read up on RLC (resistance, inductance and capacitance).

Voltage, current and resistance are related by a very simple equation: V=IR. You can arrange this equation to calculate any one of these if you know the other two, i.e. if you know voltage and resistance you can calculate current: I=V/R.

This gives you a method of indirectly measuring current since direct measurement can be tricky. Just measure the voltage drop across the resistor (put each of the probes on each end of the resistor) and divide that reading by the resistor value and you get the current going through that resistor._________________My synth build blog: http://gndsynth.blogspot.com/

the reason is the "virtual ground" on the negative input of OPAMP's
if a current flow into this input, the OPAMP try to send the same amount of current, but negative, back to the input, to keep the sum of all currents on this point at 0,00mA

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